9. Austin Research Engineers, Inc. Asphalt Concrete Overlays of Flexible Pavements: Volume 1-Devel­opment of New Design Criteria. Federal Highway Administration, Re,Pt. FHWA-RD-75-75, June 1975. NTIS: PB 263 432/7SL.

10. J. P. Zaniewski. Design Procedure for Asphalt Concrete Overlays of Flexible Pavements. Univ. of Texas at Austin, Dissertation, Dec. 1977.

89

11. R. K. Kher, w. R. Hudson, and B. F. McCullough. A Systems Analysis of Rigid Pavement Design. Center for Highway Research, Univ. of Texas at Austin, Res. Rept. 123-5, Jan. 1971.

Publication of this paper sponsored by Committee on Pavement Rehabilitation Design.

Overlay Design Based on Visible Pavement Distress N. K. Vaswani, Virginia Highway and Transportation Research Council,

Charlottesville

Data collected on 111 Interstate highway projects in Virginia were ana­lyzed by using a multiregression procedure, and the rating coefficient for each type of distress was determined. From these coefficients, the total distress and the resultant maintenance rating for each pavement were calculated. The types of distress that were found to affect the mainte­nance rating are longitudinal cracking, alligator cracking, rutting, pushing, raveling, and patching. A method for designing the required thickness of an overlay was developed based on taking the thickness equivalency of an asphalt concrete overlay in Virginia as equal to 0.5 and the overlay thickness as a function of the ratio of the traffic, in terms of the num-ber of 80-kN (18 000-lbf (18-kip)] equivalent loads, carried by the pavement before the overlay to the traffic it would carry after the over­lay, depending on the durability of the asphalt mix. This design method does not require the use of a deflection-measuring device.

In Virginia, the decision to provide an overlay over a flexible pavement conventionally is based on a visual in­spection that does not make reference to any defined criterion for pavement evaluation. However, to comply with the Reconstruction, Rehabilitation, and Resurfacing Program of the Federal Highway Administration, the states now need procedures .by which the necessity for an overlay can be validated and its required thickness can be estimated so as to obtain federal participating funds.

In Virginia and some other states, mechanistic methods for determining the required thicknesses for overlays have been developed. However, these methods are based on deflection data (!., ~) and their use would require that all districts have deflection equipment such as the Dynaflect available, along with a technician, for the collection of data. Similarly, the methods for quantifying total pavement distress based on rating sys­tems require the use of some technique for measuring distress by mechanical means. Consequently, there is a need for a method by which to establish a relation­ship between the total pavement distress, the accumu­lated traffic and the structural strength of the pavement that can be used to design overlays without the necessity of using pavement-deflection (or any other) measuring devices.

OBJECTIVE AND SCOPE

The objective of the investigation reported here was the development of a method for designing the thickness of overlays for flexible pavements that would be based on

maintenance ratings of the pavements as determined by visual observations and sound engineering judgment. These overlays would be designed for the sole purpose of improving the structural strength of the pavement. Defects in the pavement surface that did not affect its strength would not be considered.

As outlined in the working plan (3 ), the study was designed to accomplish the following tasks:

L To develop a pavement-maintenance-rating sys­tem based on the total observed pavement distress;

2. To develop a relationship between the maintenance rating, the accumulated traffic (in terms of 80-kN [ 18 000 lbf (18-kip )] equivalents}, and the structural strength of the pavement (in terms of its thickness index) that could be used to evaluate the performance of the pavement before and after the overlay;

3. To determine the thickness equivalency of the overlay; and

4. To develop a method for determining the required thickness of the overlay.

PAVEMENT-MAINTENANCE-RA TING SYSTEM

The pavement-maintenance-rating technique that was developed is based on the same principle as the ser­viceability index (SI) included in the American Associa­tion of State Highway and Officials (AASHO) Road Test results. The Sis of the new pavements at the AASHO Roar! Test varied from 3.9 to 4.5, with an average value of 4 .2. For the design of overlays in Virginia, it is proposed that a maintenance-rating factor (MR) of 100 for a new pavement be adopted. Thus, an AASHO SI of 4.2 would equal an MR of 100, and an SI of 0 would equal an MR of 0. As distress to the pavement in­creases, factors assigned to various types and degrees of distress are subtracted and the MR decreases. The MR for a new pavement will decrease from 100 as the accumulated traffic, and hence the distress, increases.

Although the pavement distress over the first few years that a road is open to traffic is so small that it is not discernible to the naked eye, it can be measured by a Dynaflect or a roughometer. However, measurement of this indiscernible distress is not necessary for the design of overlays. In the rating system developed, an SI of 3.9 or an MR of 93 [i.e., (3.9/4.2) xlOO = 93] is

90

Table 1. Interstate flexible pavement First Overlay d istress ratings and overlay data.

Pavement Distress: 1974-1975 No. of 80-kN Serial No. LC AC Ru

1 2 I 0 2 1 3 1 3 3 2 2 4 3 2 2 5 1 0 0 6 3 3 0 7 0 0 0 8 2 0 0 9 2 0 0

10 1 0 0 11 1 0 0 12 3 3 3 13 0 0 0 14 0 0 0 15 0 0 0 16 0 0 0 17 3 3 3 18 1 0 0 19 1 0 0 20 0 0 0

Note : 1 kN = 225 lbf

considered as the maximum value of incipient visible distress for the following reasons:

1. The mini'mum value of the AASHO SI for a new pavement was 3.9, which is equal to an MR of 93;

Pu

1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0

2. The rate of decrease of the MR as the traffic in­creases is constant to an MR of approximately 93 and, below that value, accelerates (i.e ., at an MR of 93, the deterioration of the pavement begins to accelerate);

3. Statistical analysis gives higher values of cor­relation coefficients when pavements that do not have visible distress are assigned an MR of 93-in the present investigation, all pavements that did not have visible distress were assigned an MR of 93, irrespective of their age, because pavements that have MRs of 93 or higher are never considered for overlays.

The types of distress that contribute to pavement deterioration are longitudinal cracking (LC), alligator cracking (AC), rutting (Ru), pushing (Pu), raveling (Ra), and patching (Pa). For these types, it is recommended that the ratings given below be adopted.

Not Very Distress Severe Severe Severe

None 0 0 0 observed

Rarely 2 3 observed

Occasionally 2 4 6 observed

Frequently 3 6 9 observed

On Interstate highways, overlays are applied while the distress is still not severe but, on low-traffic pri­mary roads, the distress may be rated severe or very severe before overlays are placed . The amount and severity of distress considered indicative of a need for an overlay will require clear specification before the rating system can be used by field engineers.

In 1974-1975, McGhee carried out a survey of 111 flexible-pavement projects on 886 km (521 miles) of the Interstate highway system and visually determined the MRs (4) shown in Table 1. A multiregression analysis based o n Equation 1 of these data, in which it is assumed that none of the distress recorded was rated as being severe,

Year Equivalent Loads Ra MR Constructed Year (000 OOOs)

0 88 1961 1971 1.55 0 78 1960 1971 2.00 0 83 1963 1977 2.72 I 83 1963 1975 2.24 0 93 1962 1975 2 .43 3 78 1963 1976 2.44 0 93 1963 1974 2 .02 0 93 1963 1974 1.97 0 93 1963 1969 1.09 2 91 1963 1969 1.16 2 91 1963 1970 1.27 0 78 1963 1976 2 .27 0 93 1964 1974 1.77 0 93 1964 1973 1.57 0 93 1964 1973 1.55 0 91 1964 1972 1.42 0 78 1965 1975 1.61 0 93 1968 0 93 1961 1969 1.36 0 93 1962 1970 1.39

MR = a0 + a1 (LC rating)+ a2 (AC rating)+ a3 (Ru rating) + a4 (Pu rating) + as( Ra rating) + a 6 (Pa rating)

D

12.3 12.3 14.0 13.8 13.8 13 .8 13.6 13.6 13.8 13 .8 13.8 13.8 13.8 13.8 13.8 13.8 13.8 15.2 13.4 13.4

(I)

gives Equation la which has a correlation coefficient of 0 .96 and standard error of 0.39.

MR= 92.6 - 2.4LC - 2.3AC - I .ORu - I .OPu - 0.9Ra (l a)

Because none of the projects on the Interstate high­ways considered had any patched areas, no coefficient for patching was included in Equation la. Patching is usually provided to cover severe or very severe dis­tress, generally in the form of alligator cracking. If patching were considered in Equation la, the coef­ficient for it would be 2.3, the same as that for alligator cracking. However, patching is here classified as not severe and is rated only by the amount observed.

The data given below, taken from serial no. 4 in Table 1, can be used to illustrate the method for de­termining the MR of a pavement.

Type of Distress Amount Severity Rating

LC Frequent Not severe 3 AC Occasional Not severe 2 Ru Occasional Not severe 2 Pu None 0 Ra Rare Not severe 1 Pa None 0

By using these data and Equation la, MR := 92 .6 -(2.4 x 3) - (2 .3 x.2) - (1.0 x 2)- {1.0 x O) - (0.9 x1) -(2.3 x O) = 77.9. None of the MRti uf lh~ 111 Inte1·state projects cited above were lower than 78.

The MRs for the 111 projects were determined in June 1975. Pavements that had values between 78 and 83 were overlaid in 1975 or 1976, except for a few that were overlaid in 1977. Thus, there is an indication that the rating system determined in the investigation is in line with field practice. However, the establish­ment of priorities based on the system might lead to improvements in the utilization of funds. As shown in Table 1, (a) one project that had an MR of 83 in 1975 was overlaid in 1977; (b)· two projects that had MRs of 78 in 1975 were overlaid in 1976; and (c) three projects that had MRs of 78, 83, and 93, respectively, were overlaid in 1975. If priorities had been established by using the rating system, the pavements that had the

91

Figure 1. Determination of number of 80-kN equivalent loads from 2 o 'o oo · O r-r-T--rTTTT-.-.,....,-r-,..,...-.....--..-..-.-..Tr.,,.-.--r-'T""""1,..,..,.--.-,......,..., traffic counts.

:>, 10,000.0

" For Buses t Take 20\ as 3 axles - 6 to 10 tires

and 80\ as 2 axles - 6 tires

~ s,ooo.o Note: 1 kN • 225 lb!. µ

"' ()

QI .... () ... ;::: QI

> c QI

> ..... tn

"' H 0 .....

"' "1J

"' 0 .... µ

" QI .... "' > ..... '.:J o" QI

z 7 0 ro

..... 0

~ z

Table 2. Thickness equivalencies of materials used in Virginia for Interstate, arterial, and primary roads.

Location Material

a, Asphalt cqncrete a, Asphalt concrete

Untreated aggregate base material (crushed or uncrushed, specification numbers 20, 21 , and 22)

Type 1 select material directly under asphalt concrete mat and over good quality subbase

a , Types 1, 2, and 3 select material In Piedmont area In Valley and Ridge area and coastal plain

Soil cement or soil lime Cement-treated aggregate base directly over

sub grade

lower MRs would have been overlaid first.

Thickness Equivalent

1.0 1.0 0.35

0.35

o.o 0.2 0. 4 0.6

The SI limits recommended by the AASHO committee (5) for use in decisions as to when overlays should be applied were correlated with the MR system as shown below.

Road Classification SI MR

Interstate .; 3.5 .; 83 Arterial .; 3.0 .; 71 Primary .; 2.5 .; 60 Low primary or " 1.5 .;36 secondary

Thus, it is seen that, for the Interstate highway pave­ments in Virginia that had MRs of 83 or less, overlays are justified. Pennsylvania has used the same ap­proach to pavement-maintenance rating (~).

1,000.0

500.0

200.0

100.0

50.0

10.0

2. 0

1. 0

0. 2

0.1

.... N 0 0 0 0 0 0 0 0 .... N 0 0 0 0 0 0 .... 0 ~ ~ ....

Humber of Vehicles in a Given Category

RELATIONSHIP BETWEEN MAINTENANCE RATING, ACCUMULATED TRAFFIC, AND STRUCTURAL STRENGrH

0 0 0 0

~ a. 0 0 .... N

The rate and amount of pavement deterioration are a function of the pavement strength and the accumulated traffic (in terms of the number of 80-kN equivalent loads) and can be determined by using Equation 2 (1)·

log no. of 80-kN equivalent loads= A+ B(thickness index)

where

(2)

A f(MR), a function of the maintenance rating and constant for a given MR value, and

B = a constant for any given MR value.

The number of 80-kN equivalent loads can be deter­mined from a traffic count by using Figur e 1 (8). The an­nual traffic counts are prepared by the Traffic-and Safety Division of the Virginia Department of Highways and Transportation (9).

The thickness-index (D) is a number that shows the intrinsic strength of the pavement (i.e., without the subgrade support). It is a nondimensional quantity and is obtained by using Equation 3 .

where

h1, lb, and h3

(3)

thicknesses of asphalt concrete sur­face layer, base layer, and subbase layer, respectively, and strength coefficients of the layers h1, lb, and h:i, respectively.

The values of a1, a2, and a3 are given in Table 2. Because there were no MR data for pavements in

92

Figure 2. Relationship between maintenance rating and cumulative traffic at different values of thickness index.

I Oil

~s

~l 0

85

"' 811 80

" 75 75

::. 711 70

" " 65

"' 65

:: (JI) bO

!: 55 e SS

~ 50 so 45 45

40 40

35 35

30 Note: 1 kN = 225 lbf. 30

ZS 2S

"' "' ~ "' " 0 0 ~

Accumulated traffic (no. or 80-kN equivalenL loads)

Figure 3. Relationship between maintenance rating and cumulative traffic of an Interstate pavement in Virginia before and after an overlay. 95 - --

bO 90 .::: ..... ~ 85 a:

" u 80 . .::: .. Actual

2. 5-cm overlay

----.-. ........ ~D 11.0 (Figure 2)

....... D=l0.6 '-

'-.::: !! 7 5 .:::

D = 10.1 ' ' ..... ' ~ 70 ' \ D = 10 \ 65 \ '\ Note: 1 cm:::: 0.4 in; 1 kN"" 225 lbf,

Virginia available for evaluation, the raw data from the AASHO Road Test pavements were used. The AASHO results give data on 270 projects that had different pavement cross sections. On each of the projects, traf­fic in terms of 80-kN equivalent loads is given for MRs of 83, 71, 60, 48, and 36 (SI values of 3.5, 3.0, 2.5, 2.0, and 1.5), respectively. The D-value index of each project was obtained by using the strength coefficients given in Table 2.

D = (l.00h1 + 0.35h2 + 0.20h3 )/2.50

(h1, h2, and h:i are measured in centimeters), and an equation based on Equation 2 had the form

(3a)

log no. of 80-kN equivalent loads= A+ 0.5(thickness index) (2a)

The values of A so obtained and the correlation coef­ficients (Rs) and standard errors (SEs) are summarized below.

MR A R SE

83 1.213 0.87 0.71 71 1.582 0.92 0.49 60 1.742 0.94 0.41 48 1.823 0.94 0.39 36 1.871 0.94 0.39

,.,

Accumulated traffic (no. of 80-kN equivalent loads)

These correlation coefficients show that an excellent relationship exists between the MR, the traffic, and the structural strength (see Figure 2).

STRENGTH COEFFICIENT

No MR data are available for overlaid pavements in Virginia; however, the AASHO Road Test gives basic data on 99 overlaid projects. These data have been evaluated and the results reported elsewhere (7). The evaluation showed that the strength coefficient of an overlay should be taken as one-half that of the asphalt concrete for new construction. In Virginia, the thick­ness equivalency of asphalt concrete for new con­struction is equal to 1 (as shown in Table 2). The strength coefficient of asphalt concrete for an overlay in Virginia is, therefore, 0.5.

Of the 111 projects analyzed in the investigation, 8 were overlaid in 1975. The average MR of these 8 projects was 83, and the average traffic on them before the overlay was about 2 million 80-kN equivalent loads. The average thickness of the overlays on these 8 projects was 2.5 cm (1 in). A 2.5-cm overlay on a new pave­ment in Virginia usually lasts as long as did the pave -ment before the overlay. Hence, it is assumed that these 8 pavements will be able to carry an additional 2 million 80-kN equivalent loads before a second overlay

Figure 4. Relationship between traffic-carrying capacity and overlay thickness.

700 ;--~~~....-~~~-..-~~~---,~~~---,

600

g 500 ,., "' .-{

" QJ

:> 0

" 400 QJ µ "-<

"' u •n "-< "-<

"' " 300 µ

c: 'M

QJ

"' "' QJ

" u 200 c: H

100

2.S 7. 5 10

Overlay th i ckne ss - cm

Table 3. Traffic growth rate and accumulated traffic (assuming 5 percent growth/year).

Period of Period of Traffic Growth Accumulated Traffic Growth Accumulated (years) Rate Traffic (years) Rate Traffic

1 I 365 11 1.62 5 169 2 1.05 748 12 1. 70 5 789 3 1.10 1 149 13 1. 78 6 438 4 1.16 1 572 14 1.87 7 120 5 1.22 2 017 15 1.97 7 839 6 1.27 2 480 16 2 .07 8 595 7 1.34 2 969 17 2 . 17 9 387 8 l. 40 3 480 18 2.28 10 219 9 1.47 4 016 19 2.39 11 091

10 1.54 4 578 20 2.51 12 007

is needed. The relationship of the MRs to the traffic history of the average of these 8 pavements is shown on an exaggerated scale in Figure 3, which shows that the averages of the thickness indices of these 8 pavements before and after the overlays were 10. 1 and 10.6, re­spectively. Thus, a 2.5-cm overlay gives a strength coefficient of 10.6 - 10. 1 (or 0.5). Hence, it appears that the conclusion reached in the evaluation of the overlay strength coefficient for AASHO road projects (1) could also be applied to overlays in Virginia.

TIIlCKNESS OF AN OVERLAY

By using Equation 2a, the traffic carried by an overlaid pavement can be calculated as

Traffic= antilog(Aa + 0.5Da) - an tilog(Ab + 0.5Db) (4)

93

where

Ab and Aa = constants for the MR before the overlay and at the end of the overlay service and

Da and Db = thickness indices of the pavement be­fore and after the overlay.

As described above, for a given type of highway, the MRs before the overlay and at the end of the overlay service are the same; that is, Aa =Ab. In such a case, Equation 4 reduces to

Traffic after overlay = traffic before overlay

x : antilog (0.5 (overlay thickness/2 .5)

x thickness equivalency of overlay] - n (4a)

(when overlay thickness is measured in centimeters) or

Traffic after overlay /traffic before overlay =

[antilog (0.1 x overlay thickness) - l]

or

Percentage increase in traffic after overlay =

[an tilog (overlay thickness/ 10) - I ] x I 00

(4b)

(4c)

Figure 4, which is based on Equation 4c, shows the percentage increase in the number of 80-kN equivalent loads versus the overlay thickness in centimeters and can be used to determine the required thickness of an overlay. This figure shows that the traffic capacities for overlay thicknesses of 2.5, 5.1, and 7.6 cm (1, 2, and 3 in) are, respectively, 78, 217, and 464 percent of the traffic before the overlay.

Deflection studies carried out before and after the application of asphalt concrete overlays have shown that overlay thicknesses of 2. 5 cm or more do contribute to an increase in the structural strength of the pavement. It is therefore recommended that the overlays provided for increasing the structural strength of pavements be a minimum of 2.5 cm thick. The following method is recommended for designing the thickness of an overlay.

The design for the thickness of an overlay is de­pendent on the durability of the asphalt concrete mix used and the way it is affected by such factors as age, hardening, and stripping of the asphalt. An overlay made from a properly placed, well-designed mix can perform satisfactorily for 10-15 years without surface rejuvenation. For determining the required thickness of an overlay, the use of a 12-year service life for the mix is recommended. The procedure for determining the overlay thickness is· as follows:

1. Determine the accumulated traffic in terms of the number of 80-kN equivalent loads that the pavement has carried from the date of construction to the date of the proposed overlay, irrespective of any previous overlays. If necessary, use Figure 1 to convert the traffic count into 80-kN equivalent loads.

2. Determine the accumulated traffic in terms of the number of 80-kN equivalent loads the pavement will carry in the 12 years following the overlay.

3. From Figure 4, determine the thickness of the overlay for a given percentage increase in traffic after the overlay, taking the percentage increase as (number of 80-kN equivalent loads after the overlay + number of 80-kN equivalent loads before the overlay) x 100.

For an Interstate highway pavement that had been built in 1967 and had a maintenance rating of 76.5 in

94

1977 an overlay probably would be justified. The thickness of the overlay can be calculated as outlined below.

1. (a) Determine the daily traffic in 80-kN equiv­alent loads. From the average daily traffic (ADT) volume records published annually, obtain the ADT for 1976 and use these data and Figure 1 to calculate the num-ber of 80-kN equivalent loads as shown below.

Type of Vehicle

Two axle, 6 tire Three axle, 10 tire Trailer trucks Buses (assume 20

percent three-axle and 80 percent two­axle vehicles)

Total

ADT

320 50

2850 40

No. of 80-kN Equivalent Loads

58 14

2500 6

2578

(In these calculations, automobiles and two-axle, four­tire vehicles are not considered because their damaging effect on the pavement is almost negligible.) Thus, for a four-lane highway, the design traffic = 2578 x0.5 x 0.8 = one thousand thirty-one 80-kN equivalent loads, where the reported traffic counts include both directions of travel, one-half the reported traffic is assumed to travel in each direction, and 80 percent of the truck traffic is assumed to use the outside (design) lane. (b) Determine the accumulated traffic before the over­lay. These data can be determined f:om the traffic . records or estimated on the assumption that the traffic has increased as the rate of 5 percent/year (a widely accepted standard) by using Table 3, which gives the growth rate for each year for a 20-year period (e.g., the ADT after 9 years = 1.47 xADT during the first year) and the accumulated traffic for each year for a 20-year period (the accumulated traffic after 9 years = 4016 x ADT during the first year). Thus, in the above example, the accumulated traffic o~ the road in 1977 (i.e., at the end of 11 years of service and before the overlay) =design daily traffic in 1977 x accumulated traffic rate .;- growth rate = 1031 x 5169 .;-1. 62 = 3.29 million 80-kN equivalent loads.

2. Determine the accumulated traffic after the overlay. From the daily traffic just before the overlay (i.e., 2578 equivalent loads), the traffic to be carried by the overlay is 2578 x accumulated traffic rate (12 years) .;- growth rate (12 years) = 2578 x 5789 .;-1. 70 = 8.78 million 80-kN equivalent loads.

3. Determine the overlay thickness. The required overlay thickness can be determined by using Figure 4. The percentage increase in daily traffic to be sustained by the overlay is (8. 78 million 7 3 .29 million) x 100 = 267 percent and the required overlay thickness is ap­proximately 130 mm (5.1 in).

CONCLUSIONS

1. A simplified method based on visual inspections can provide uniformity in decisions regarding the stages at

which pavements would be overlaid in an economical manner.

2. In Virginia, the thickness equivalency for an asphalt concrete overlay is 0.5.

3. A method for designing the thickness of overlays has been developed.

ACKNOWLEDGMENT

The research reported here was conducted under the general supervision of Jack H. Dillard of the Virginia Highway and Transportation Research Council. It was carried out as part of a Federally Coordinated Program project with funds administered by the Federal Highway Administration. The opinions, findings, and conclusions expressed are mine and not necessarily those of the sponsoring agencies.

REFERENCES

1. Pavement Rehabilitation: Proceedings of a Work­shop. Federal Highway Administration, Rept. FHWA-RD-74-60, June 1974. NTIS: PB 246 801/ 5ST.

2. Austin Research Engineers, Inc. Asphalt Concrete Overlays of Flexible Pavements: Volume 1-De­velopment of New Design Criteria. Federal Highway Administration, Rept. FHWA-RD-75-75, June 1975. NTIS: PB 263 432/7SL.

3. N. K. Vaswani. Working Plan: Design of Overlays Based on Pavement Condition, Roughness, and Deflections. Virginia Highway and Transportation Research Council, Charlottesville, Rept. VHTRC 77-WP20, April 1977.

4. K. H. McGhee. A Review of Pavement Performance on Virginia's Interstate System. Virginia Highway and Transportation Research Council, Charlottewille, Rept. VHTRC 77-R24, Nov. 1976.

5. AASHO Committee on Design. Interim Guide for the Design of Flexible Pavement Structures. AASHO, Oct. 12, 1961.

6. A. C. Bhajandas and others. A Practical Approach to Flexible· Pavement Evaluation and Rehabilitation. Proc., 4th International Conference on Structural Design of Asphalt Pavements, Univ. of Michigan, Ann Arbor, Vol. 1, 1977, pp. 665-673.

7. N. K. Vaswani. Design of Overlays for Flexible Pavements Based on AASHO Road Test Results. Virginia Highway and Transportation Research Council, Charlottesville, Rept. VHTRC 78-R37, Feb. 1978.

8. N. K. Vaswani. Estimation of 18-Kip Equivalent on Primary and Interstate Road Systems in Virginia. HRB, Highway Research Record 466, 1973, pp. 82-95.

9. Average Daily Traffic Volumes on Interstate, Arterial, and Primary Roads. Virginia Department of Highways and Transportation, 1976.

Publication of this paper sponsored by Committee on Pavement Rehabilitation Design.